### Abstract

A unital, that is, a block-design 2−(q^{3}+1,q+1,1), is embedded in a projective plane Π of order q^{2} if its points and blocks are points and lines of Π. A unital embedded in PG(2,q^{2}) is Hermitian if its points and blocks are the absolute points and non-absolute lines of a unitary polarity of PG(2,q^{2}). A classical polar unital is a unital isomorphic, as a block-design, to a Hermitian unital. We prove that there exists only one embedding of the classical polar unital in PG(2,q^{2}), namely the Hermitian unital.

Original language | English |
---|---|

Pages (from-to) | 67-75 |

Number of pages | 9 |

Journal | Journal of Combinatorial Theory. Series A |

Volume | 153 |

DOIs | |

Publication status | Published - Jan 1 2018 |

### Fingerprint

### Keywords

- Embedding
- Finite Desarguesian plane
- Hermitian curve
- Unital

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

### Cite this

^{2}).

*Journal of Combinatorial Theory. Series A*,

*153*, 67-75. https://doi.org/10.1016/j.jcta.2017.08.002

**Embedding of classical polar unitals in PG(2,q ^{2}).** / Korchmáros, Gábor; Siciliano, Alessandro; Szőnyi, T.

Research output: Contribution to journal › Article

^{2})',

*Journal of Combinatorial Theory. Series A*, vol. 153, pp. 67-75. https://doi.org/10.1016/j.jcta.2017.08.002

^{2}). Journal of Combinatorial Theory. Series A. 2018 Jan 1;153:67-75. https://doi.org/10.1016/j.jcta.2017.08.002

}

TY - JOUR

T1 - Embedding of classical polar unitals in PG(2,q2)

AU - Korchmáros, Gábor

AU - Siciliano, Alessandro

AU - Szőnyi, T.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - A unital, that is, a block-design 2−(q3+1,q+1,1), is embedded in a projective plane Π of order q2 if its points and blocks are points and lines of Π. A unital embedded in PG(2,q2) is Hermitian if its points and blocks are the absolute points and non-absolute lines of a unitary polarity of PG(2,q2). A classical polar unital is a unital isomorphic, as a block-design, to a Hermitian unital. We prove that there exists only one embedding of the classical polar unital in PG(2,q2), namely the Hermitian unital.

AB - A unital, that is, a block-design 2−(q3+1,q+1,1), is embedded in a projective plane Π of order q2 if its points and blocks are points and lines of Π. A unital embedded in PG(2,q2) is Hermitian if its points and blocks are the absolute points and non-absolute lines of a unitary polarity of PG(2,q2). A classical polar unital is a unital isomorphic, as a block-design, to a Hermitian unital. We prove that there exists only one embedding of the classical polar unital in PG(2,q2), namely the Hermitian unital.

KW - Embedding

KW - Finite Desarguesian plane

KW - Hermitian curve

KW - Unital

UR - http://www.scopus.com/inward/record.url?scp=85028596969&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85028596969&partnerID=8YFLogxK

U2 - 10.1016/j.jcta.2017.08.002

DO - 10.1016/j.jcta.2017.08.002

M3 - Article

VL - 153

SP - 67

EP - 75

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

SN - 0097-3165

ER -